Slot antenna



Aug. 10, 1954 H. BOSSE SLOT ANTENNA v Filed Jan. 30, 1952 Fig. 1

A Rmax 0,:

2 Sheets-Sheet 1 Fig.2

INVEN TOR ATTORNEY Aug. 10, 1954 H. BOSSE 2,686,265

SLOT ANTENNA Filed Jan. 30, 1952 2 Sheets-Sheet 2 Fig.3

z 1 T R s L 7; 16

22 Lmax I Lmax Wave 611/05 INVEINTVOR ATTORNEY Patented Aug. 10, 1954 was SLOT ANTENNA Heinrich Bosse, Stuttgart-Gablenberg, Wurttemberg-Baden, Germany, assignor to International Standard Electric Corporation, New York, N. Y., a corporation of Delaware Application January 30, 1952, Serial No. 269,016

Claims priority, application Germany January 31, 1951 2 Claims. 1

This invention relates to slot antennas and particularly to slot antennas in hollow waveguides.

It is known that the characteristics of an antenna are usually determined by the normal frequency, the bandwidth, the voltage standing wave ratio (VSWR), and the power gain over the frequency band to be transmitted. The normal frequency bandwidth may be defined as the ratio of the bandwidth in terms of frequency to another given frequency, characterizing the absolute position of the frequency band, e. g., the lower frequency limit. The VSWR is the value indicating the extent of match between the antenna and its feed line. The power gain is a measure of the concentration of radiated energy at a certain point and is defined by the ratio of the power to be fed to a standard antenna and the power to be fed to the antenna under consideration.

It is realized by those experienced in the art, that the requirements imposed on the antenna, with respect to these three quantities, incurs considerable difiiculty, because of the interdependency of these quantities.

It is also known that in slot antennas these quantities depend in large degree on the length of the slot. If the slot is in a plane surface which is large with respect to the operating wavelengths, the slot acts similarly to a dipole of equal length. Although there exists an analogy between the surface type slot antenna and the dipole, there is little analogy between the slot antenna in a waveguide and the dipole.

It is the object of this invention to provide a slot antenna in a waveguide constructed in accordance with a formula which will simplify the construction and improve operating conditions of the antenna.

The above-mentioned and other features and objects of this invention and the manner of attaining them will become more apparent and the invention itself Will be best understood, by reference to the following description of an embodiment of the invention taken in conjunction with the accompanying drawings, wherein:

Fig. 1 shows an impedance curve of an antenna slot in a plane surface; and

Fig. 2 shows a curve in which power gain is plotted against frequency for a slot antenna in a Waveguide.

Fig. 3 shows a curve indicating the relationship between the different relative wavelengths appearing at the slot antenna.

Fig. l shows a wave guide having a slot antenna in the surface thereof.

Referring first to a slot antenna in a plane surface it may be seen from Figure 1 that the input impedance of such a slot is a complex function of the frequency and takes the form substantially of a loop. In deriving this curve, the frequency was considered the parameter and the slot length maintained constant. The point F05 corresponds to half-wave feed and point F1 to full-wave feed; therefore the frequency in this case is F1=2.Fo.5.

When an antenna comprising a slot in a hollow waveguide is used for wide band radiations, a compromise is necessitated between the frequency bandwidth and the minimum mismatch. This compromise may be achieved without undue power loss by controlling the length, cross section, and capacity of the slot. For most practical purposes, it may be assumed that the limits of the minimum power gain fall on the points of the half-Wave and full-wave feed of the slot in the waveguide. Actually, these limiting points are slightly outside the feed points as will become obvious from the following considerations taken in conjunction with Figure 2.

In accordance with my invention, these dimensions may be determined by use of the formula developed hereinbelow.

In developing the formula for a slot antenna in a hollow waveguide, it first must be realized that the wave in the feed line corresponds to the free wavelength A and the slot-wavelength A The latter is that wavelength arising along the slot. Of course A always exceeds x, and the ratio depends on the periphery and width of the Waveguide and slot respectively.

The wavelength A in the guide determines the distribution of the power along the slot. For example, if the slot is fed with a wavelength and if the ratio of the radiating effect of the slot in terms of dipoles is approximately three half-wave dipoles, arranged in stacked relationship. Of course, certain differences are apparent which are largely due to the fact that the current decreases at the edges of the slot in a sinusoidal manner towards the end thereof. The input impedance of such a slot describes a curve similar to a slot in 'a plane surface. The difference is that the frequency parameters in the latter case are displaced in accordance with the ratio M, and therefore the frequency F1 is no longer twice the frequency F05.

Since radiation damping is effected by increasing the length of the slot, the loop characteristic of the input impedance of the waveguide type slot becomes smaller. To this end the entire loop of the impedance characteristic may be made to form a circle indicating a given allowable mismatch. Thus the operating range is no longer achieved by the limits of the allowable mismatch as in the case of the dipole or surface type slot but rather by the minimum power gain desired. As is shown qualitatively in Figure 2 the power gain increases continuously beginning at the point of half-wave feed as the frequency increases and reaches a maximum around the fullwave feed and increases thereafter. In order that the power gain should not fall below a certain limit indicated in Figure 2 by a dotted horizontal line the operational frequency must be kept between the wavelength i max and R The corresponding points are also marked on Figure 1. It may be seen that the reduction in size of the input impedance characteristic by virtue of increased damping and increased slot length of the antenna cannot be driven to arbitrary limits because the frequency range between the allowable limits becomes steadily smaller due to the increasing ratio For a desired wave band Ax an optimum slot length 2111 will exist, at which the wave range will coincide with the allowable range between K feeding and feeding and the mismatch will become a minimum. If the slot is chosen shorter than the optimum length the VSWR throughout the band will be reduced and the useful wave band Ax will fall short of the desired value. In deriving the dimensions of the antenna the frequency bands should be made to agree even in their absolute values and therefore the waveguide tube periphery, the slot width, and to a certain extent the thickness of the wall of the tube effective slot capacity surface must be considered. These factors determine the wave length i in the guide and its relation to the free space wavelength X The above mentioned conditions may be achieved if the ratio,

is a constant where Z is the slot length and lm is the optimum slot length. Referring to Figure 1 in order for An max to fall on Fo.5, I) should equal 2. The relationship of the optimum slot length,

thus

c constant If A min and A mm are chosen to fall on the points F05 and F1 then a is 0.5.

The above described mathematical formula may be explained as follows:

The ratio is chosen such that the desired free space wavelength M shown in the impedance characteristic curve of Figure 1, falls as accurately as possible on the waveguide range corresponding to the quantity a achieved from Figure 2, and extending from i min to A This characterizes the maximum allowable limits of the loop of the impedance characteristic curve of Figure l and thus the possible minimum VSWR. As to the relationship of A X is about hyperbolical with A extending to infinity at the point of the cut-off wavelength A the required normalized free space wave range has to be shifted as far as possible so, that the corresponding band width at the slot approaches the point of infinity corresponding to the cut-off wavelength K without departing from the requirements of bandwidth and power gain. This is the case when the ratio M2 min XR mux a The result therefrom is then is made to match the given absolute values. The aforementioned ratio which is shown in Figure 3 results to It is obvious for many purposes to imagine the slot antenna being a great plurality of stacked individual little loop-antennas, parallel-connected and fed from the edges of the slot acting as a feeder line. Then the cut-off" wavelength to is equal to the resonant wavelength 21l'C'\/LqCq of such a loop-antenna, Lq and Cq being the actual inductivity and capacity respectively. Hence A depends upon the dimensions of the slot antenna, on the other hand it is easy to find the most favourable dimension of the slot an tenna if A is known with the aid of the diagram shown in Figure 3.

Let us now describe the way to proceed when wishing to dimension a slot antenna according to my invention. Assume as a numerical example the range between 8'7.5 to me. This corresponds to a free space wave band from M. max=3.4:3 meters to AL min-=3 meters. With these values we obtain from the above equation p=0ll25 and with the values p=2 and a=0.5 approaching ideal conditions 0:156. By multiplying this value with M. max=3143 meters we finally obtain the optimum slot length of about Zm=5.4 meters. While the wavelength in the uide shifts between the half wave and the full wave point and a=0.5 it changes in the ratio of 1:2 while the free space wavelength shifts only in the ratio of 121.15 thus it is realized that the curve of the function is very steep and that, )\L=f()xR), is near cut-off.

The dimension of the slot antenna, namely both its inductivity and its capacity, has to be adapted to this optimum slot length. This may be achieved with the aid of the diagram shown in Figure 3. In case of feeding the slot, for instance, with a frequency corresponding to the maximum free space wavelength A there will be, according to the aforementioned statements, a slot feeding of corresponding to the said ordinate is marked by the vertical interrupted line lying at 0.95. Hence the cutoff wavelength A will be 3.62 meters, and therewith it may be easy to find, in a known manner and according to the above explanations, an inductivity and capacity of the antenna, which are most suitable for all given practical conditions. I

Whilst this application of the diagram outlined in Figure 3 is very simple since the validity of this diagram is a universal one, it is, of course, also possible to calculate the value of A directly from this formula, which then would have conveniently to be written as follows:

1 )\L max AR max Naturally, also in this case there exist equivalent formulas employing the minimum wave lengths or any other characteristic wavelengths.

It is of course, obvious that several slots proportioned in accordance with the invention may exist on a wave guide for better directional gain or for obtaining particular radiation patterns. These slots may be fed at any relative amplitude and phases as may be suitable for the desired application. If the slots are one above the other the dimensions will not cha ge as comp e t a single slot but if they are colinear one will have to consider the effect of capacitive reactance and the consequent effect on the ratio v optimum slot length maximum free space wave length wave length band width p max1mum free space wave length maximum wave length at the slot minimum Wave length at the slot b maximum wave length at the slot slot length 2. A wave guide, having a slot antenna in its surface thereof, formed in accordance with the formula defined in claim 1, said wave guide having a cut-off wavelength A determined in accordance with the following formula L max R max wherein 1 =maximum free space wavelength.

R =maximum wavelength at the slot.

References Cited in the file of this patent UNITED STATES PATENTS Number Name Date 2,297,202 Dallenbach et el. Sept. 29, 1942 2,482,162 Feldman Sept. 20, 1949 OTHER REFERENCES The design of a wave-guide-fed-array of slots to give a specified radiation pattern, by Cullen et al., Journal of Institution of Electrical Engineers, vol. 93, Part III-A, N0. 4, May 1946. Copy in Div. 51.

Resonant Slots, by Watson, Journal of Institution of Electrical Engineers, vol. 93, Part III-A, No, y 19 C py Div.- 51. 

